Class 8 Area of a Trapezium — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The formula for the area of a trapezium with parallel sides a and b and height h is:
A21 x (a + b) x h
B(a + b) x h
C21 x a x b x h
Da x b x h
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Answer: A) 21 x (a + b) x h
Area of a trapezium = 21 x (sum of parallel sides) x (height) = 21(a + b)h.
2. The area of a trapezium is 200 sq m and the sum of its parallel sides is 40 m. Find its height (in m).
A9
B20
C10
D11
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Answer: C) 10
200 = 21(40)h = 20h, so h = 20200 = 10 m.
3. A trapezium has parallel sides 9 cm and 15 cm and area 96 sq cm. Find its height (in cm).
A9
B7
C16
D8
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Answer: D) 8
96 = 21(9 + 15)h = 12h, so h = 1296 = 8 cm.
4. The shape of the gable end of a house is a trapezium. The longer parallel side (base) is 8 m, the shorter (top) is 4 m, and the height is 3 m. What is its area (in sq m)?
A18 sq m
B24 sq m
C12 sq m
D36 sq m
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Answer: A) 18 sq m
Area = 21(8 + 4)(3) = 21(12)(3) = 18 sq m.
5. A trapezium has an area of 360 sq cm and a height of 12 cm. Its parallel sides differ by 4 cm. Find the lengths of the two parallel sides (shorter, longer in cm).
A28 cm and 32 cm
B26 cm and 34 cm
C30 cm and 30 cm
D27 cm and 33 cm
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Answer: A) 28 cm and 32 cm
360 = 21(a + b)(12) = 6(a + b), so a + b = 60. With b - a = 4: a = 28, b = 32 cm.